The response of piezoelectric face plates used in ultrasonic imaging systems

The amplitude and phase responses of piezoelectric face plates used in ultrasonic imaging systems are analyzed. These elements are assumed to be of arbitrary thickness, thereby making the analysis very general and applicable to any practical situation. The analysis is based on a plane-wave approach and takes into account the complex modes of wave propagation (including evanescent waves) within a piezoelectric medium, resulting from the interaction between acoustic and electric fields and from the special crystallographic symmetryo f the medium. The response is then calculated in terms of the charge produced on the interfaces of the piezoelectric element with water (or any other suitable acoustic coupling medium) and with air when the interface with water is struck by an angular spectrum of plane ultrasonic waves. Computer plots of response versus plane-wave spectrum are presented. These curves make it possible to calculate the theoretically attainable resolution of the image and the aberrations introduced into it by the piezoelectric element when other components of the imaging systems are perfect. The resolution of a typical system and the aberrations introduced by the piezoelectric element are calculated. These results compare favorably with experimental data.